Vibration analysis of piezoelectric graphene platelets micro-plates

Document Type : Research Article


1 Faculty of Engineering, Shahrekord University, Shahrekord, Iran

2 Department of Mechanical Engineering, Faculty of Engineering, Shahrekord University


Free and forced vibration analyses of micro-plates reinforced with graphene platelets integrated with piezoelectric layers are presented. For thermo-electrical vibration examination, a uniform temperature field and a constant external electric field along the thicknesses of the piezoelectric layers are considered. On the other hand, a uniform in-plane load is regarded along the micro-plate edges for a mechanical free vibration analysis. The Halpin–Tsai micromechanical model is used to estimate the material properties of each layer of the graphene platelets of core layer. A convergence examination is conducted to reach a functionally graded dispersion of graphene platelets layers despite the implementation of several individual graphene platelets layers. Four different distribution patterns of graphene platelets are considered to examine the vibration features for simply-supported boundary condition employing Navier’s technique. Several numerical studies are accomplished to demonstrate the effects of the weight fraction, the distribution pattern, the width and the length of the graphene platelets besides the material length scale parameter, the thickness of the piezoelectric layers, the micro-plate length to the core layer thickness ratio, the applied voltage, the temperature change and the in-plane force on the natural frequencies and the time history response. The results demonstrate that in thermal environment not only reinforcing with graphene platelets does not improve the structural stiffness but also deteriorates it.


Main Subjects

1. M.A. Farsangi, A. Saidi, R. Batra, Analytical solution for free vibrations of moderately thick hybrid piezoelectric laminated plates, Journal of Sound and Vibration, 332(22) (2013) 5981-5998.
2. Y. Kiani, Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers, Computers & Mathematics with Applications, 72(9) (2016) 2433-2449.
3. M. Bouazza, A.M. Zenkour, Vibration of carbon nanotube-reinforced plates via refined nth-higher-order theory, ARCHIVE OF APPLIED MECHANICS, (2020)
4. H.-S. Shen, Y. Xiang, F. Lin, Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments, Computer Methods in Applied Mechanics and Engineering, 319 (2017) 175-193.
5. M. Song, S. Kitipornchai, J. Yang, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Composite Structures, 159 (2017) 579-588.
6. E. Garcia-Macias, L. Rodriguez-Tembleque, A. Saez, Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates, Composite Structures, 186 (2018) 123-138.
7. R. Gholami, R. Ansari, Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates, Engineering Structures, 156 (2018) 197-209.
8. S. Qaderi, F. Ebrahimi, V. Mahesh, Free vibration analysis of graphene platelets–reinforced composites plates in thermal environment based on higher-order shear deformation plate theory, International Journal of Aeronautical and Space Sciences, 20(4) (2019) 902-912.
9. F. Pashmforoush, Statistical analysis on free vibration behavior of functionally graded nanocomposite plates reinforced by graphene platelets, Composite Structures, 213 (2019) 14-24.
10. A.R. Saidi, R. Bahaadini, K. Majidi-Mozafari, On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading, Composites Part B: Engineering, 164 (2019) 778-799.
11. W. Chen, X. Li, A new modified couple stress theory for anisotropic elasticity and microscale laminated Kirchhoff plate model, Archive of Applied Mechanics, 84(3) (2014) 323-341.
12. Y.-G. Wang, W.-H. Lin, C.-L. Zhou, Nonlinear bending of size-dependent circular microplates based on the modified couple stress theory, Archive of Applied Mechanics, 84(3) (2014) 391-400.
13. Y. Yue, K. Xu, Z. Tan, W. Wang, D. Wang, The influence of surface stress and surface-induced internal residual stresses on the size-dependent behaviors of Kirchhoff microplate, Archive of Applied Mechanics, 89(7) (2019) 1301-1315.
14. S.-R. Li, H.-K. Ma, Analysis of free vibration of functionally graded material micro-plates with thermoelastic damping, Archive of Applied Mechanics, 90 (2020) 1285–1304.
15. F. Abbaspour, H. Arvin, Vibration and thermal buckling analyses of three-layered centrosymmetric piezoelectric microplates based on the modified consistent couple stress theory, Journal of Vibration and Control, 26(15-16)  (2020) 1253-1265.
16. M. Arefi, M. Kiani, A.M. Zenkour, Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST, Journal of Sandwich Structures & Materials, 22(1) (2020) 55-86.
17. H. Arvin, The flapwise bending free vibration analysis of micro-rotating Timoshenko beams using the differential transform method, Journal of Vibration and Control, 24(20) (2018) 4868-4884.
18. J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, CRC press, 2003.
19. Q. Wang, On buckling of column structures with a pair of piezoelectric layers, Engineering structures, 24(2) (2002) 199-205.
20. H. Wu, S. Kitipornchai, J. Yang, Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates, Materials & Design, 132 (2017) 430-441.
21. Y. Huang, Z. Yang, A. Liu, J. Fu, Nonlinear buckling analysis of functionally graded graphene reinforced composite shallow arches with elastic rotational constraints under uniform radial load, Materials, 11(6) (2018) 910.
22. L. Meirovitch, Principles and techniques of vibrations, Prentice Hall Upper Saddle River, NJ, 1997.
23. N.V. Nguyen, J. Lee, H. Nguyen-Xuan, Active vibration control of GPLs-reinforced FG metal foam plates with piezoelectric sensor and actuator layers, Composites Part B: Engineering, 172 (2019) 769-784.
24. E. Jomehzadeh, H. Noori, A. Saidi, The size-dependent vibration analysis of micro-plates based on a modified couple stress theory, Physica E: Low-dimensional Systems and Nanostructures, 43(4) (2011) 877-883.
25. M. Shariyat, Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties, Composite Structures, 88(2) (2009) 228-239.